Numerical Modeling and Simulation of Mineral Dissolution in Fractured Carbonate Formations

Mineral dissolution plays important role in many subsurface transport processes including waterflooding, geological CO2 sequestration (GCS), and matrix acidizing in carbonate formations. Such a dissolution process could form the preferential pathways to cause a failure of waterflooding and GCS due to the early breakthrough of the displacing fluid and CO2 leakage, and it could also dramatically affect the efficiency of the matrix acidizing treatment due to the different dissolution patterns. Consequently, a mathematical model that accurately describes the dynamic behavior of fracture evolution and dissolution patterns is essential for better design waterflooding, GCS, and matrix acidizing. In this study, we have developed a mathematical model that couples the Stokes-Brinkman equation and reactive transport equations to describe the coupled processes of fluid flow, solute transport, and chemical reactions in both single and multiple mineral systems. Compared to Darcy’s equation, the Stokes-Brinkman equation is a unified approach for modeling fluid flow in both porous media and free flow regions, which is an ideal candidate for modeling of porosity alteration and fracture enhancement due to mineral dissolution. We have developed and implemented a numerical procedure that solves the Stokes-Brinkman equation and the reactive transport equations in a sequential fashion. In the proposed numerical procedure, the Stokes-Brinkman equation is solved by a mixed finite element method for the 2-D flow and solved by a staggered grid finite difference method for the 3-D flow. The reactive transport equations are solved by an implicit control volume finite difference method. Numerical validation and experiments have been performed using the proposed numerical solution procedure. The numerical results demonstrate that the proposed mathematical model is capable of modeling the coupled processes of fluid flow, solute transport, chemical reactions, and alterations of rock properties under both linear and radial flow for in fractured porous media. And the mineral volume fractions, rock heterogeneity, flow conditions, and reaction rate are the dominant factors in alterations of rock properties and fracture evolution.